A Graphical Formalism for Mixed Multi-Unit Combinatorial Auctions
Andrea Giovannucci, Jesús Cerquides, Ulle Endriss, Juan A. Rodríguez-Aguilar
Abstract:
Mixed Multi-Unit Combinatorial Auctions are auctions that allow
participants to bid for bundles of goods to buy, for bundles of goods
to sell, and for transformations of goods. The intuitive meaning of a
bid for a transformation is that the bidder is offering to produce a
set of output goods after having received a set of input goods. To
solve such an auction the auctioneer has to choose a set of bids to
accept and decide on a sequence in which to implement the associated
transformations. Mixed auctions can potentially be employed for the
automated assembly of supply chains of agents. However, mixed auctions
can be effectively applied only if we can also ensure their
computational feasibility without jeopardising optimality. To this
end, we propose a graphical formalism, based on Petri nets, that
facilitates the compact represention of both the search space and the
solutions associated with the winner determination problem for mixed
auctions. This approach allows us to dramatically reduce the number of
decision variables required for solving a broad class of mixed auction
winner determination problems. An additional major benefit of our
graphical formalism is that it provides new ways to formally analyse
the structural and behavioural properties of mixed auctions.